Algorithmic Self-Assembly of DNA Sierpinski Triangles

Algorithms and information, fundamental to technological and biological organization, are also an essential aspect of many elementary physical phenomena, such as molecular self-assembly. Here we report the molecular realization, using two-dimensional self-assembly of DNA tiles, of a cellular automaton whose update rule computes the binary function XOR and thus fabricates a fractal pattern—a Sierpinski triangle—as it grows. To achieve this, abstract tiles were translated into DNA tiles based on double-crossover motifs. Serving as input for the computation, long single-stranded DNA molecules were used to nucleate growth of tiles into algorithmic crystals. For both of two independent molecular realizations, atomic force microscopy revealed recognizable Sierpinski triangles containing 100–200 correct tiles. Error rates during assembly appear to range from 1% to 10%. Although imperfect, the growth of Sierpinski triangles demonstrates all the necessary mechanisms for the molecular implementation of arbitrary cellular automata. This shows that engineered DNA self-assembly can be treated as a Turing-universal biomolecular system, capable of implementing any desired algorithm for computation or construction tasks

Doctor of Philosophy

dissertationUbiquitin is a small protein which interacts with other proteins as a post-translational modification and as a binding partner for proteins which contain a ubiquitin binding domain (UBD). Proteins modified with ubiquitin are often targeted for degradation. Ubiquitin regulates both soluble and membrane-bound proteins in cells of nearly all tissues. Here we use mathematical models to study three distinct regulatory systems involving ubiquitin: regulation of the yeast uracil transporter, Fur4, protein sorting mediated by the endosomal sorting complexes required for transport (ESCRTs), and regulation of Rad18 in the DNA damage tolerance pathway. Using a differential equation model of Fur4 regulation, we demonstrate that deubiquitination and retention are essential roles of the Rsp5/Ubp2 complex localized to the endosome. We also predict a nearly constant pool of endosomal Fur4 independent of extracellular conditions. ESCRTs are responsible for sorting ubiquitinated proteins (cargo) on the endosomal membrane prior to formation of intralumenal vesicles. However, the mechanisms of sorting remain unclear. Motivated by recent experimental data, we present a cellular automata model of ESCRT sorting which demonstrates that a flexible network of ESCRTs and cargoes is sufficient for high efficiency sorting under specified rules. ESCRT-cargo networks exist on membranes while all ESCRT binding studies consider ESCRT interactions in solution. We present novel results on the dimensional dependence of dissociation constants for general protein-protein interactions using stochastic methods. We present a conversion for transforming three-dimensional dissociation constants to two-dimensional dissociation constants and demonstrate that ESCRT-cargo interactions are more stable on membranes than in solution. Using our computed two-dimensional reaction rates, we present an ODE model for the evolution of the size of ESCRT-cargo networks. Our results suggest that ESCRT-mediated sorting can be achieved on the order of seconds. Lastly, we examine ubiquitin-dependent regulation of Rad18 in the DNA damage tolerance pathway, a system of strictly soluble proteins which does not rely on ubiquitin-dependent degradation. Results of ODE models suggest that the dissociation constants for Rad18 binding events must be measured in order to better understand the mechanisms behind damage-specific responses

Minimal model of self-replicating nanocells: a physically embodied information-free scenario

The building of minimal self-reproducing systems with a physical embodiment (generically called protocells) is a great challenge, with implications for both theory and applied sciences. Although the classical view of a living protocell assumes that it includes information-carrying molecules as an essential ingredient, a dividing cell-like structure can be built from a metabolism-container coupled system, only. An example of such a system, modeled with dissipative particle dynamics, is presented here. This article demonstrates how a simple coupling between a precursor molecule and surfactant molecules forming micelles can experience a growth-division cycle in a predictable manner, and analyzes the influence of crucial parameters on this replication cycle. Implications of these results for origins of cellular life and living technology are outlined.Comment: 9 pages, 10 figure

Computational methods and tools for protein phosphorylation analysis

Signaling pathways represent a central regulatory mechanism of biological systems where a key event in their correct functioning is the reversible phosphorylation of proteins. Protein phosphorylation affects at least one-third of all proteins and is the most widely studied posttranslational modification. Phosphorylation analysis is still perceived, in general, as difficult or cumbersome and not readily attempted by many, despite the high value of such information. Specifically, determining the exact location of a phosphorylation site is currently considered a major hurdle, thus reliable approaches are necessary for the detection and localization of protein phosphorylation. The goal of this PhD thesis was to develop computation methods and tools for mass spectrometry-based protein phosphorylation analysis, particularly validation of phosphorylation sites. In the first two studies, we developed methods for improved identification of phosphorylation sites in MALDI-MS. In the first study it was achieved through the automatic combination of spectra from multiple matrices, while in the second study, an optimized protocol for sample loading and washing conditions was suggested. In the third study, we proposed and evaluated the hypothesis that in ESI-MS, tandem CID and HCD spectra of phosphopeptides can be accurately predicted and used in spectral library searching. This novel strategy for phosphosite validation and identification offered accuracy that outperformed the other currently existing popular methods and proved applicable to complex biological samples. And finally, we significantly improved the performance of our command-line prototype tool, added graphical user interface, and options for customizable simulation parameters and filtering of selected spectra, peptides or proteins. The new software, SimPhospho, is open-source and can be easily integrated in a phosphoproteomics data analysis workflow. Together, these bioinformatics methods and tools enable confident phosphosite assignment and improve reliable phosphoproteome identification and reportin

Combining causal Bayes nets and cellular automata: A hybrid modelling approach to mechanisms

Causal Bayes nets (CBNs) can be used to model causal relationships up to whole mechanisms. Though modelling mechanisms with CBNs comes with many advantages, CBNs might fail to adequately represent some biological mechanisms because—as Kaiser ([2016]) pointed out— they have problems with capturing relevant spatial and structural information. In this article we propose a hybrid approach for modelling mechanisms that combines CBNs and cellular automata. Our approach can incorporate spatial and structural information while, at the same time, it comes with all the merits of a CBN representation of mechanisms

Mathematical modeling of immunological reactions

3. Models of HIV infection and other infectious diseases 4. Models of T cell activation and proliferatio

Simulations of Computing by Self-Assembly

Winfree (1996) proposed a Turing-universal model of DNA self-assembly. In this abstract model, DNA double-crossover molecules self-assemble to form an algorithmically-patterned two-dimensional lattice. Here, we develop a more realistic model based on the thermodynamics and kinetics of oligonucleotide hydridization. Using a computer simulation, we investigate what physical factors influence the error rates, i.e., when the more realistic model deviates from the ideal of the abstract model. We find, in agreement with rules of thumb for crystal growth, that the lowest error rates occur at the melting temperature when crystal growth is slowest, and that error rates can be made arbitrarily low by decreasing concentration and increasing binding strengths